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Seminar

Lunch with Hamilton: A new necessary and sufficient condition for the stability of linear Hamiltonian systems with periodic coefficients September 12, 2018 (12:00 PM PDT - 01:00 PM PDT)
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Location: MSRI: Baker Board Room
Speaker(s) Hong Qin (Princeton University; University of Science and Technology of China)
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Abstract/Media

Linear Hamiltonian systems with periodic coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. I will show that the solution map of a linear Hamiltonian system with periodic coefficients can be parameterized by an envelope matrix, which has a clear physical meaning and satisfies a nonlinear envelope matrix equation. The Hamiltonian system is stable if and only if the envelope matrix equation admits a periodic (matched) solution. The mathematical devices utilized in this theoretical development with significant physical implications are time-dependent canonical transformations, normal forms and Iwasawa decomposition of symplectic matrices.

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